Question

Suppose your car accelerates from rest to 9 m/s in 2 s. Assume that the acceleration is constant in this time interval. A. What is the acceleration of your car? Express your answer in m/s 2 . B. How far will you travel in 2 s? Express your answer in meters.

Answer 1

The acceleration of the car is 4.5 m/s² and the car will travel 18 meters in 2 seconds.

Step-by-step explanation:

A. What is the acceleration of your car?

To find the acceleration, we can use the formula:

acceleration = (final velocity - initial velocity) / time

Plugging in the given values, we get:

acceleration = (9 m/s - 0 m/s) / 2 s = 4.5 m/s²

Therefore, the acceleration of your car is 4.5 m/s².

B. How far will you travel in 2 s?

To find the distance traveled, we can use the formula:

distance = initial velocity * time + 0.5 * acceleration * time²

Since the car starts from rest, the initial velocity is 0 m/s. Plugging in the given values, we get:

distance = 0 * 2 + 0.5 * 4.5 * 2² = 0 + 0.5 * 4.5 * 4 = 4.5 * 4 = 18 meters

Therefore, you will travel 18 meters in 2 seconds.

Answer 2

(a) The acceleration of the car is,
`4.5m/s^2`

(b) The distance covered by the car is, 9 m

Explanation :

By the 1st equation of motion,

`v=u+at` ...........(1)

where,

v = final velocity = 9 m/s

u = initial velocity = 0 m/s

t = time = 2 s

a = acceleration of the car = ?

Now put all the given values in the above equation 1, we get:

`9m/s=0m/s+a* (2s)`

`a=4.5m/s^2`

The acceleration of the car is,
`4.5m/s^2`

By the 2nd equation of motion,

`s=ut+(1)/(2)at^2` ...........(2)

where,

s = distance covered by the car = ?

u = initial velocity = 0 m/s

t = time = 2 s

a = acceleration of the car =
`4.5m/s^2`

Now put all the given values in the above equation 2, we get:

`s=(0m/s)* (2s)+(1)/(2)* (4.5m/s^2)* (2s)^2`

By solving the term, we get:

`s=9m`

The distance covered by the car is, 9 m